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1.
Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting. 相似文献
2.
This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691–708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid–gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy’s law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton’s method. 相似文献
3.
Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K r2), and the specific storage of the formation zone (S s2) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness (r s). 相似文献
4.
This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K
s and the shape parameter vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented. 相似文献
5.
6.
In this paper, we propose multilevel Monte Carlo (MLMC) methods that use ensemble level mixed multiscale methods in the simulations of multiphase flow and transport. The contribution of this paper is twofold: (1) a design of ensemble level mixed multiscale finite element methods and (2) a novel use of mixed multiscale finite element methods within multilevel Monte Carlo techniques to speed up the computations. The main idea of ensemble level multiscale methods is to construct local multiscale basis functions that can be used for any member of the ensemble. In this paper, we consider two ensemble level mixed multiscale finite element methods: (1) the no-local-solve-online ensemble level method (NLSO); and (2) the local-solve-online ensemble level method (LSO). The first approach was proposed in Aarnes and Efendiev (SIAM J. Sci. Comput. 30(5):2319-2339, 2008) while the second approach is new. Both mixed multiscale methods use a number of snapshots of the permeability media in generating multiscale basis functions. As a result, in the off-line stage, we construct multiple basis functions for each coarse region where basis functions correspond to different realizations. In the no-local-solve-online ensemble level method, one uses the whole set of precomputed basis functions to approximate the solution for an arbitrary realization. In the local-solve-online ensemble level method, one uses the precomputed functions to construct a multiscale basis for a particular realization. With this basis, the solution corresponding to this particular realization is approximated in LSO mixed multiscale finite element method (MsFEM). In both approaches, the accuracy of the method is related to the number of snapshots computed based on different realizations that one uses to precompute a multiscale basis. In this paper, ensemble level multiscale methods are used in multilevel Monte Carlo methods (Giles 2008a, Oper.Res. 56(3):607-617, b). In multilevel Monte Carlo methods, more accurate (and expensive) forward simulations are run with fewer samples, while less accurate (and inexpensive) forward simulations are run with a larger number of samples. Selecting the number of expensive and inexpensive simulations based on the number of coarse degrees of freedom, one can show that MLMC methods can provide better accuracy at the same cost as Monte Carlo (MC) methods. The main objective of the paper is twofold. First, we would like to compare NLSO and LSO mixed MsFEMs. Further, we use both approaches in the context of MLMC to speedup MC calculations. 相似文献
7.
Emanuela Bianchi Janetti Monica Riva Alberto Guadagnini 《Computational Geosciences》2016,20(3):555-565
We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K i j,r , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K i j,r reduce to a set of nine scalar quantities, K i j,r . Our results show that K i j,r of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K i j,r of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K i j,r with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases. 相似文献
8.
Jinxi Song Weiwei Jiang Shaofeng Xu Guotao Zhang Liping Wang Min Wen Bo Zhang Yuanyuan Wang Yongqing Long 《Hydrogeology Journal》2016,24(8):2049-2062
Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In this study, the heterogeneity of hydraulic conductivity and Darcian flux in a submerged streambed and its adjacent exposed stream banks were investigated in the Beiluo River, northwest China. In the submerged streambed, Darcian flux was estimated by measurement of vertical hydraulic conductivity (K v) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (K h) and K v were measured by on-site permeameter tests. In the submerged streambed, K v values gradually decreased with depth and the higher values were concentrated in the center and close to the erosional bank. Compared to the exposed stream banks, the K v values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the K h values increased on the erosional bank, while they decreased on the depositional bank. The values of VHG along the thalweg illustrate that downwelling flux occurred in the deepest area while upwelling flux appeared in the other areas, which might result from the change of streambed elevation. The higher value of the Darcian flux in the submerged streambed existed near the erosional bank. 相似文献
9.
Firouz Rosti Murad Abu-Farsakh Jongwon Jung 《Geotechnical and Geological Engineering》2016,34(4):1119-1134
This paper presents the numerical simulation of pile installation and the subsequent increase in the pile capacity over time (or setup) after installation that was performed using the finite element software Abaqus. In the first part, pile installation and the following load tests were simulated numerically using the volumetric cavity expansion concept. The anisotropic modified Cam-Clay and Dracker–Prager models were adopted in the FE model to describe the behavior of the clayey and sandy soils, respectively. The proposed FE model proposed was successfully validated through simulating two full-scale instrumented driven pile case studies. In the second part, over 100 different actual properties of individual soil layers distracted from literature were used in the finite element analysis to conduct parametric study and to evaluate the effect of different soil properties on the pile setup behavior. The setup factor A was targeted here to describe the pile setup as a function of time after the end of driving. The selected soil properties in this study to evaluate the setup factor A include: soil plasticity index (PI), undrained shear strength (S u ), vertical coefficient of consolidation (C v ), sensitivity ratio (S r ), and over-consolidation ratio (OCR). The predicted setup factor showed direct proportion with the PI and S r and inverse relation with S u , C v and OCR. These soil properties were selected as independent variables, and nonlinear multivariable regression analysis was performed using Gauss–Newton algorithm to develop appropriate regression models for A. Best models were selected among all based on level of errors of prediction, which were validated with additional nineteen different site information available in the literature. The results indicated that the developed model is able to predict the setup behavior for individual cohesive soil layers, especially for values of setup factor greater than 0.10, which is the most expectable case in nature. 相似文献
10.
11.
Stabilized single-point 4-node quadrilateral element for dynamic analysis of fluid saturated porous media 总被引：2，自引：0，他引：2
An accurate and efficient low-order quadrilateral mixed u?Cp element suitable for dynamic analysis of fluid saturated porous media is presented. The element uses physical hourglass stabilization to facilitate single-point integration for the solid phase, and non-residual stabilization of the fluid phase to circumvent instability in the incompressible-impermeable limit due to the use of equal-order interpolation for the displacement and pressure fields. Element behavior is verified and demonstrated through several numerical examples. 相似文献
12.
A new OH maser was detected in January 2008 toward the infrared source IRAS 05338-0624 in the dark cloud L1641N. The observations were carried out on the Nan cay Radio Telescope (France) in the 1667 and 1665 MHz OH lines. In the spectra of both lines, thermal OH emission from the surrounding molecular cloud is present at radial velocities V LSR = 6–9 km/s. In addition, a narrow maser feature is present in both lines at V LSR = 2 km/s in the profiles obtained on January 7, 2008; the peak flux densities at 1667 and 1665 MHz are 1.5 and 0.4 Jy, respectively. No OH maser emission was detected in February–July 2008. Then, a maser feature was again observed in the 1665 MHz line on August 20, 2008, at the same velocity as in January, V LSR = 2 km/s, with a peak flux density of 0.4 Jy. No 1667 MHz counterpart was observed with an upper limit of ～0.1 Jy. Emission in both OH lines was again absent on September 18. The source was also observed in the H2O line at λ = 1.35 cm on the 22-m radio telescope of the Pushchino Radio Astronomy Observatory (Russia) on February 7 and 13, 2008. In both cases, a maser feature was detected at V LSR = 9 km/s, with peak flux densities of 35 and 15 Jy, respectively. After the its apparent absence in April, H2O maser emission reappeared on May 14, 2008, at V LSR = 7 km/s with a flux density of about 15 Jy. The history of previous observations of the object in the OH and H2O lines is traced. The maser displays strong and rapid flux variability in the lines of both molecules, as is typical of young low-luminosity stellar objects at early stages of their evolution. 相似文献
13.
Shankar Mitra 《Contributions to Mineralogy and Petrology》1976,59(2):203-226
The Weverton quartzites in the Maryland Blue Ridge are deformed by one major period of greenschist-grade deformation. The components of finite strain due to different independent mechanisms have been measured for these rocks. The total strain is split up into two major components: $$\varepsilon ^t = \varepsilon ^p + \varepsilon ^d .$$ The finite natural strain caused by dislocation creep (? d ) is measured by a new technique using folded and stretched rutile needles which are good strain markers within the quartz crystals. Pressure solution strain (? p ) is measured from the ratio of the area of new crystals and fibers to the whole rock area in principal sections. Grain boundary sliding is a dependent process which accompanies both mechanisms. Pressure solution obeys a linear Newtonian flow law, \(\left| {\dot \gamma _0^p } \right| = A_p \left| {\tau _0 } \right|\) , while dislocation creep obeys a power law of the form \(\left| {\dot \gamma _0^d } \right| = A_d \left| {\tau _0 } \right|^n \) where \(\dot \gamma _0^p ,\dot \gamma _0^d \) are octahedral shear strain rates, τ0 is the octahedral shear stress and A p , A p and n are constants. A direct correlation between finite strain measurements and the operating flow laws can be made. Application of these methods and principles to a few field examples indicates that the rocks obey a flow law partly governed by each mechanism. Any set of physical conditions defines a unique flow law and there is a transition in creep behavior from dominantly Newtonian to a power law with increasing strain rate. 相似文献
14.
Dispersive mass transport processes in naturally heterogeneous geological formations (porous media) are investigated based on a particle approach to mass transport and on its numerical implementation using LPT3D, a Lagrangian Particle Tracking 3D code. We are currently using this approach for studying microscale and macroscale space–time behavior (advection, diffusion, dispersion) of tracer plumes, solutes, or miscible fluids, in 1,2,3-dimensional heterogeneous and anisotropic subsurface formations (aquifers, petroleum reservoirs). Our analyses are based on a general advection-diffusion model and numerical scheme where concentrations and fluxes are discretized in terms of particles. The advection-diffusion theory is presented in a probabilistic framework, and in particular, a numerical analysis is developed for the case of advective transport and rotational flows (numerical stability of the explicit Euler scheme). The remainder of the paper is devoted to the behavior of concentration, mass flux density, and statistical moments of the transported tracer plume in the case of heterogeneous steady flow fields, where macroscale dispersion occurs due to geologic heterogeneity and stratification. We focus on the case of perfectly stratified or multilayered media, obtained by generating many horizontal layers with a purely random transverse distribution of permeability and horizontal velocity. In this case, we calculate explicitly the exact mass concentration field C(x,
t), mass flux density field f(x, t), and moments. This includes spatial moments and dispersion variance 2
x
(t) on a finite domain L, and temporal moments on a finite time scale T, e.g., the mass variance of arrival times 2
T
(x). The moments are related to flux concentrations in a way that takes explicitly into account finite space–time scales of analysis (time-dependent tracer mass; spatially variable flow through mass). The multilayered model problem is then used in numerical experiments for testing different ways of recovering information on tracer plume migration, dispersion, concentration and flux fields. Our analyses rely on a probabilistic interpretation that emerges naturally from the particle approach; it is based on spatial moments (particle positions), temporal moments (mass weighted arrival times), and probability densities (both concentrations and fluxes). Finally, as an alternative to direct estimations of the flux and concentration fields, we formulate and study the Moment Inverse Problem. Solving the MIP yields an indirect method for estimating the space–time distribution of flux concentrations based on observed or estimated moments of the plume. The moments may be estimated from field measurements, or numerically computed by particle tracking as we do here. 相似文献
15.
Shijian Liu 《GeoJournal》1994,34(1):47-54
Debris flow is a natural phenomenon which occurs on steep slopes of mountain regions. Very often morainic material and nonmorainic sediments, such as debris flow material, fluvial and other sediments, are mixed in the marginal mountain systems of the Tibetan Plateau. The study of quartz-grain surface features of debris flow has an important significance for differentiating between different origins of Quaternary sediments. Features of quartz-grain in debris flow will be described as below:
- The predominant shapes of quartz grains are irregular.
- The degree of roundness of grains is in general are angular to subangular in shape.
- The textures of quartz-grains in debris flows are conchoidal fractures, parallel steps and mechanical V-marks. Parallel steps are especially abundant. Their presence is the most characteristic indicator of debris flow sand, aiding in the differentiation between debris flow and glacial sand.
- Fresh cleavage planes are extremely flat.
16.
Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines 总被引：1，自引：0，他引：1
AMIR HAMZEH HAGHIABI 《Journal of Earth System Science》2016,125(5):985-995
In this paper, multivariate adaptive regression splines (MARS) was developed as a novel soft-computing technique for predicting longitudinal dispersion coefficient (DL) in rivers. As mentioned in the literature, experimental dataset related to DL was collected and used for preparing MARS model. Results of MARS model were compared with multi-layer neural network model and empirical formulas. To define the most effective parameters on DL, the Gamma test was used. Performance of MARS model was assessed by calculation of standard error indices. Error indices showed that MARS model has suitable performance and is more accurate compared to multi-layer neural network model and empirical formulas. Results of the Gamma test and MARS model showed that flow depth (H) and ratio of the mean velocity to shear velocity (u/u?) were the most effective parameters on the DL. 相似文献
17.
We present a new normalization for the linear density-perturbation spectrum in a multi-parameter model of the Universe. Using the differential mass function for the nearly galaxy clusters obtained from optical data, we have constructed a functional relation between the dispersion of the density contrast σ 8 on the scale 8h ?1 Mpc and the cosmological parameters Ω m , ΩΛ, h, n, f v for each of three theoretical approximations of the mass function: Press-Schechter, Sheth-Tormen and Jenkins. An extended class of models of the Universe with general spatial curvature include four parameters for the matter components: baryons (Ω b ), “cold” dark matter (Ω c ), “hot” dark matter (Ω v ), and the vacuum energy (ΩΛ). It is shown that the most accurate normalization of the power spectrum is achieved with the Sheth-Tormen approximation. 相似文献
18.
Ángel Rodríguez-Rozas David Pardo Carlos Torres-Verdín 《Computational Geosciences》2018,22(5):1271-1281
We develop a rapid 2.5-dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary high-order \(H^{1}\)- and \(\mathbf {H}\)(curl)-conforming spatial discretizations. It solves problems where material properties remain constant along one spatial direction, over which we consider a Fourier series expansion and each Fourier mode is solved independently. We propose a novel a priori method to construct quasi-optimal discretizations in physical and Fourier space. This construction is based on examining the analytical (fundamental) solution of the 2.5D formulation over multiple homogeneous spaces and assuming that some of its properties still hold for the 2.5D problem over a spatially heterogeneous formation. In addition, a simple parallelization scheme over multiple measurement positions provides efficient scalability. Our method yields accurate borehole logging simulations for realistic synthetic examples, delivering simulations of borehole resistivity measurements at a rate faster than 0.05 s per measurement location along the well trajectory on a 96-core computer. 相似文献
19.
Connectivity patterns of heterogeneous porous media are important in the estimation of groundwater residence time distributions (RTDs). Understanding the connectivity patterns of a hydraulic conductivity ( \(K\) ) field often requires knowledge of the entire aquifer, which is not practical. As such, the method used to estimate unknown \(K\) values using known \(K\) values is important. This study investigates how varying levels of conditioning data and four simulation techniques, one multi-Gaussian and three multi-point, are able to recreate key \(K\) field features and connectivity patterns of a synthetic two-dimensional bimodal distributed ln( \(K\) ) field with highly connected high \(K\) features. These techniques are then assessed in the context of RTD estimation. It was found that the multi-Gaussian technique presented a bias towards earlier travel times with increased conditioning data. This was due to the inability of the method to recreate multiple scales of connecting features. Of the multi-point methods investigated, the facies method was unable to predict early arrival times. The use of a continuous variable training image produced good fits to the observed residence time distribution with a high number of conditioning points. The ability of the methods to predict the shape of residence time distributions appears to be related to their ability to reproduce the connection patterns of higher \(K\) features. 相似文献
20.
The construction of deep railway tunnels requires the prediction of natural temperatures at depth. Geothermal data for the Alps are presented and principles of previously employed methods to predict temperatures, using Andreae's analytical approach, are discussed. We then use a finite element numerical model based on pure conduction to calculate temperatures at depth. This method allows rock heterogeneity and anisotropy to be taken into account.This model is applied to the Maurienne-Ambin tunnel project, a 55 km long tunnel between St-Jean-de-Maurienne (France) and Susa (Italy), which will be the longest tunnel for the planned TGV (high speed train) Lyon-Torino link. Data from several deep boreholes (10 total, with 3>1000 m) are used to provide essential parameters for the model, i.e.:
相似文献
| – | - geological structure; |
| – | - geothermal gradients; |
| – | - rock conductivities from cores; |
| – | - geothermal deep heat flow. |